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%I A253358 #69 Feb 20 2024 17:36:41
%S A253358 3,3,3,9,5,3
%N A253358 Decimal expansion of Sum_{n>=1} prime(n)/n^3.
%C A253358 Since prime(n) ~ n*log(n), Sum_{n>=1} prime(n)/n^j converges for j > 2.
%e A253358 3.339530...
%e A253358 The first few partial sums are:
%e A253358 up to prime(n)=2, 2/1^3 = 2.0;
%e A253358 up to prime(n)=3, 2 + 3/2^3 = 2.375;
%e A253358 up to prime(n)=5, 2 + 3/2^3 + 5/3^3 = 2.56018;
%e A253358 The partial sum for n <= 100000 is 3.3393903401...
%e A253358 The partial sum for n <= 1000000 is 3.33951457002...
%e A253358 The partial sum for n <= 5000000 is 3.3395274693...
%e A253358 The partial sum for n <= 10000000 is 3.339529222...
%e A253358 The partial sum for prime(n) <= 999999937 is 3.33953071535199...
%Y A253358 Cf. A253357 (sum over prime(n)/n^4).
%K A253358 nonn,cons,more
%O A253358 1,1
%A A253358 _Olivier Izad_, Dec 30 2014

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